| Description: |
This course is about asymptotic methods for finding approximate solutions to linear and nonlinear ordinary differential
equations, as well as for approximately evaluating integrals. To quote Bender and Orszag: In contrast to methods which we would describe as exact, rigorous, systematic, limited in scope and deadly, these new methods are approximate, intuitive, heuristic, powerful and fascinating.
Much undergraduate work on differential equations is concerned with exact analytical solutions. However, differential equations arise in the course of modelling the real world, and often are not amenable to exact methods. In MATH 461, approximate methods which are powerful enough to be used on nonlinear problems are studied. Techniques allow characterization of singular solution behaviour, often necessary before solving numerically. Some background in complex variables is useful
|
